The core is not designed to have any currents flow through it. It is however a conducting loop that experiences a changing magnetic field. It will therefore have small currents induced in it/ These are called as eddy current.
The core is laminated to reduce these to a minimum as they interfere with the efficient transfer of energy from the primary cell to secondary one. The eddy currents cause energy to be lost from the transformer as they heat up the core i.e., the electrical energy is being wasted as unwanted heat energy.